Basic deformation theory of smooth formal schemes |
| |
Authors: | Marta Pé rez Rodrí guez |
| |
Affiliation: | Departamento de Matemáticas, Escola Superior de Enxeñería Informática, Campus de Ourense, Universidad de Vigo, E-32004 Ourense, Spain |
| |
Abstract: | We provide the main results of a deformation theory of smooth formal schemes as defined in [L. Alonso Tarrío, A. Jeremías López, M. Pérez Rodríguez, Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes, Comm. Algebra 35 (2007) 1341-1367]. Smoothness is defined by the local existence of infinitesimal liftings. Our first result is the existence of an obstruction in a certain Ext1 group whose vanishing guarantees the existence of global liftings of morphisms. Next, given a smooth morphism f0:X0→Y0 of noetherian formal schemes and a closed immersion Y0?Y given by a square zero ideal I, we prove that the set of isomorphism classes of smooth formal schemes lifting X0 over Y is classified by and that there exists an element in which vanishes if and only if there exists a smooth formal scheme lifting X0 over Y. |
| |
Keywords: | Primary, 14B10 secondary, 14A15, 14B20, 14B25, 14F10 |
本文献已被 ScienceDirect 等数据库收录! |
|